A New Variational Model for Binary Classification in the Supervised Learning Context

We examine the supervised learning problem in its continuous setting and give a general optimality condition through techniques of functional analysis and the calculus of variations. This enables us to solve the optimality condition for the desired function u numerically and make several comparisons with other widely utilized supervised learning models. We employ the accuracy and area under the receiver operating characteristic curve as metrics of the performance. Finally, 3 analyses are conducted based on these two mentioned metrics where we compare the models and make conclusions to determine whether or not our method is competitive.